Structural and electronic properties of graphite layers grown on SiC(0 0 0 1)

Photoelectron spectroscopy, low-energy electron diffraction, and scanning probe microscopy were used to investigate the electronic and structural properties of graphite layers grown by solid state graphitization of SiC(0 0 0 1) surfaces. The process leads to well-ordered graphite layers which are rotated against the substrate lattice by 30°. On on-axis 6H-SiC(0 0 0 1) substrates we observe graphitic layers with up to several 100 nm wide terraces. ARUPS spectra of the graphite layers grown on on-axis 6H-SiC(0 0 0 1) surfaces are indicative of a well-developed band structure. For the graphite/n-type 6H-SiC(0 0 0 1) layer system we observe a Schottky barrier height of ?_B,n = 0.3 ± 0.1 eV. ARUPS spectra of graphite layers grown on 8° off-axis oriented 4H-SiC(0 0 0 1) show unique replicas which are explained by a carpet-like growth mode combined with a step bunching of the substrate.     

Adaptive Algorithm for Constrained Least-Squares Problems

This paper is concerned with the implementation and testing of an algorithm for solving constrained least-squares problems. The algorithm is an adaptation to the least-squares case of sequential quadratic programming (SQP) trust-region methods for solving general constrained optimization problems. At each iteration, our local quadratic subproblem includes the use of the Gauss–Newton approximation but also encompasses a structured secant approximation along with tests of when to use this approximation. This method has been tested on a selection of standard problems. The results indicate that, for least-squares problems, the approach taken here is a viable alternative to standard general optimization methods such as the Byrd–Omojokun trust-region method and the Powell damped BFGS line search method.     

Possible Loss and Recovery of Gibbsianness¶During the Stochastic Evolution of Gibbs Measures

We consider Ising-spin systems starting from an initial Gibbs measure ν and evolving under a spin-flip dynamics towards a reversible Gibbs measure μ≠ν. Both ν and μ are assumed to have a translation-invariant finite-range interaction. We study the Gibbsian character of the measure νS(t) at time t and show the following: (1) For all ν and μ, νS(t) is Gibbs for small t. (2) If both ν and μ have a high or infinite temperature, then νS(t) is Gibbs for all t > 0. (3) If ν has a low non-zero temperature and a zero magnetic field and μ has a high or infinite temperature, then νS(t) is Gibbs for small t and non-Gibbs for large t. (4) If ν has a low non-zero temperature and a non-zero magnetic field and μ has a high or infinite temperature, then νS(t) is Gibbs for small t, non-Gibbs for intermediate t, and Gibbs for large t. The regime where μ has a low or zero temperature and t is not small remains open. This regime presumably allows for many different scenarios. Received: 26 April 2001 / Accepted: 10 October 2001     

Electrical conduction and dielectric properties of vanadium phosphate glasses doped with lithium

AC conductivity and dielectric studies on vanadium phosphate glasses doped with lithium have been carried out in the frequency range 0.2-100 kHz and temperature range 290-493 K. The frequency dependence of the conductivity at higher frequencies in glasses obeys a power relationship, σ_ac=Aω^s. The obtained values of the power s lie in the range 0.5≤s≤1 for both undoped and doped with low lithium content which confirms the electron hopping between V⁴⁺ and V⁵⁺ ions. For doped glasses with high lithium content, the values of s≤0.5 which confirm the domination of ionic conductivity. The study of frequency dependence of both dielectric constant and dielectric loss showed a decrease with increasing frequency while they increase with increasing temperature. The results have been explained on the basis of frequency assistance of electron hopping besides the ionic polarization of the glasses. The bulk conductivity increases with increasing temperature whereas decreases with increasing lithium content which means a reduction of the V⁵⁺.     

Mod 2 cohomology of combinatorial Grassmannians

Matroid bundles, introduced by MacPherson, are combinatorial analogues of real vector bundles. This paper sets up the foundations of matroid bundles. It defines a natural transformation from isomorphism classes of real vector bundles to isomorphism classes of matroid bundles. It then gives a transformation from matroid bundles to spherical quasifibrations, by showing that the geometric realization of a matroid bundle is a spherical quasifibration. The poset of oriented matroids of a fixed rank classifies matroid bundles, and the above transformations give a splitting from topology to combinatorics back to topology. A consequence is that the mod 2 cohomology of the poset of rank k oriented matroids (this poset classifies matroid bundles) contains the free polynomial ring on the first k Stiefel-Whitney classes.     

Monte Carlo study of interfacial silicon suboxide layers and oxidation kinetics

A simple simulation scheme that simultaneously describes the growth kinetics of SiO₂ films at the nanometer scale and the SiO_x/Si interface dynamics (its extent, and spatial/temporal evolution) is presented. The simulation successfully applies to experimental data in the region above and below 10 nm, reproduces the Deal and Grove linear-parabolic law and the oxide growth rate enhancement in the very thin film regime (the so-called anomalous region). According to the simulation, the oxidation is governed mainly by two processes: (a) the formation of a transition suboxide layer and (b) its subsequent drift towards the silicon bulk. We found that it is the superposition of these two processes that produces the crossover from the anomalous oxidation region behavior to the linear-parabolic law.     

Algebraic methods in quantum mechanics: from molecules to polymers

We present a brief review of algebraic techniques developed and applied in molecular spectroscopy in the last five years. We also outline perspectives for new applications of the Lie algebraic method in the first decade of the new century. Received 21 November 2001     

Metastability in the Potts model on the Cayley tree

Metastability in the ferromagneticp-state Potts model defined on the Cayley tree is discussed. It is shown that the sign of the boundary fieldH _s determines the order of the transition as well as the stability of the low-temperature phase. Lowering the temperature withH _s >0, a system withp<2 (p>2) will display a second (first)-order transition to a metastable (stable) phase. ForH _s >0 a second (first)-order transition to a metastable (stable) phase occurs ifp>2 (p<2). In this case the system also has a residual entropy which is negative forp<2.     

Diffraction in a nonlinear defocusing medium

Diffraction by a semitransparent screen is considered in the framework of the nonlinear Schrödinger equation. The case of a defocusing medium is investigated. The method used represents a synthesis of the method of Riemann's matrix problem and the technique of Whitham's deformations of spectral curves.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Vol. 179, pp. 23–31, 1989.